Conjugate-cut loci and injectivity domains on two-spheres of revolution
In a recent article [B. Bonnard, J.-B. Caillau, R. Sinclair and M. Tanaka, 26 (2009) 1081–1098], we relate the computation of the conjugate and cut loci of a family of metrics on two-spheres of revolution whose polar form is = d + ()d to the period mapping of the -variable. One purpose of this article is to use this relation to evaluate the cut and conjugate loci for a family of metrics arising as a deformation of the round sphere and to determine the convexity properties...